Area and perimeter worksheets (rectangles and squares) - Free Printable

Let’s solve each problem one by one. We’ll find either the Area (A) or Perimeter (P) as asked.

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Problem 1: Pentagon with sides 3 cm, 4 cm, 3 cm, 2 cm, 6 cm

We are asked for Perimeter (P) → add all side lengths.

3 + 4 = 7
7 + 3 = 10
10 + 2 = 12
12 + 6 = 18

✔ P = 18 cm

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Problem 2: Rectangle 2 in by 7 in

Asked for Area (A) and Perimeter (P)

- Area = length × width = 7 × 2 = 14 in²
- Perimeter = 2×(length + width) = 2×(7+2) = 2×9 = 18 in

✔ A = 14 in², P = 18 in

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Problem 3: Regular octagon? All sides labeled 3 cm? Wait — only one side is labeled “3 cm”, but it looks like a regular octagon (all sides equal). Since no other info, we assume all 8 sides are 3 cm.

Asked for Perimeter (P) → 8 sides × 3 cm = 24 cm

✔ P = 24 cm

*(Note: If it’s not regular, we can’t solve — but since only one side is given and it’s symmetric, we assume regular.)*

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Problem 4: Rectangle 97 mm by 40 mm

Asked for Area (A) and Perimeter (P)

- Area = 97 × 40
Let’s compute:
97 × 40 = (100 - 3) × 40 = 4000 - 120 = 3880 mm²

- Perimeter = 2×(97 + 40) = 2×137 = 274 mm

✔ A = 3880 mm², P = 274 mm

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Problem 5: Rectangle 13 cm by 4 cm

Asked for Area (A) and Perimeter (P)

- Area = 13 × 4 = 52 cm²
- Perimeter = 2×(13 + 4) = 2×17 = 34 cm

✔ A = 52 cm², P = 34 cm

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Problem 6: L-shaped figure

Break into two rectangles:

Top rectangle: 8 cm wide × 3 cm high → area = 8×3 = 24 cm²
Bottom rectangle: 2 cm wide × 6 cm high → area = 2×6 = 12 cm²
Total Area = 24 + 12 = 36 cm²

Now Perimeter: trace outer edges.

Start from top left:
→ right 8 cm
↓ down 3 cm
← left 6 cm (since bottom part is only 2 cm wide, so 8 - 2 = 6 cm overhang)
↓ down 6 cm
← left 2 cm
↑ up 9 cm total height? Wait — let’s list all outer sides carefully.

Actually, better to count all outer segments:

Top: 8 cm
Right top: 3 cm
Then inward left: 6 cm (because bottom part starts at 2 cm from left, so 8 - 2 = 6 cm)
Down: 6 cm
Left: 2 cm
Up: 9 cm? No — total height is 3 + 6 = 9 cm, but we already went down 3 and then 6, so going back up must be 9 cm? That doesn’t make sense.

Wait — let’s draw mentally:

The shape is like:

```
___________
| | 3 cm
|_________|
| |
| | 6 cm
|_____|
2 cm
```

So full outline:

Start at top-left corner:

→ Right 8 cm
↓ Down 3 cm
← Left 6 cm (to where the vertical part starts)
↓ Down 6 cm
← Left 2 cm
↑ Up 9 cm (total height: 3+6=9)
→ Right 8 cm? No — that would double count.

Better way: use grid method or add all outer sides.

List of outer sides:

Top: 8 cm
Right side (top part): 3 cm
Inner horizontal (leftward): 6 cm (from x=8 to x=2)
Vertical down: 6 cm
Bottom: 2 cm
Left side (full height): 9 cm (3+6)
But wait — when you go up the left side, you’re covering the entire left edge.

Actually, perimeter path:

Start at top-left:

1. Right → 8 cm
2. Down → 3 cm
3. Left → 6 cm (now at x=2, y=3)
4. Down → 6 cm (to y=9)
5. Left → 2 cm (to x=0, y=9)
6. Up → 9 cm (back to start)

That’s all? But step 6 goes up 9 cm — yes, because total height is 9 cm.

Add them: 8 + 3 + 6 + 6 + 2 + 9 = let’s compute:

8+3=11; 11+6=17; 17+6=23; 23+2=25; 25+9=34 cm

Wait — is that correct? Let me check another way.

Alternative: imagine the bounding box is 8 cm wide and 9 cm tall → perimeter of rectangle would be 2*(8+9)=34 cm. But our shape has an indentation? Actually, no — in this case, the L-shape does NOT have any internal corners that reduce perimeter — actually, the perimeter is same as the bounding rectangle? No!

Wait — in this specific L-shape, if you look:

Original rectangle 8x9 would have perimeter 34 cm.

Our shape removes a rectangle of 6 cm wide and 6 cm high from the bottom right? No — actually, it’s added on the bottom left? I think I messed up.

Looking again at diagram description:

It says:

Top bar: 8 cm long, 3 cm high
Below it, centered? Or aligned left? The diagram shows:

“8 cm” on top, then below it on the right side “3 cm” (height of top bar), then below that “5 cm”? Wait — original problem says:

In image: for problem 6, it shows:

Top rectangle: width 8 cm, height 3 cm
Attached below it on the left? Or right? The label says “5 cm” on the right side of the lower part? Wait — user wrote:

“6. A = ___, P = ___” and in text: “8 cm” on top, “3 cm” on right of top part, then “5 cm” on right of lower part? Wait no — let me re-read user input.

User wrote for problem 6:

“8 cm
3 cm
5 cm
6 cm
2 cm”

And it's an L-shape. Probably:

- Top horizontal: 8 cm
- Right vertical of top part: 3 cm
- Then the lower part sticks out to the left? Or right?

Actually, standard interpretation: it's a T or L shape. Given labels:

Probably:

The top bar is 8 cm wide, 3 cm tall.
Below it, attached to the left side, is a vertical bar 2 cm wide and 6 cm tall.
And there’s a label “5 cm” — maybe the distance from right end of top bar to right end of bottom bar? Not clear.

Wait — perhaps the “5 cm” is the height of the lower part? But it says “6 cm” too.

Looking back at user’s text:

For problem 6: “8 cm” (top), “3 cm” (right side of top), “5 cm” (maybe the gap?), “6 cm” (height of stem), “2 cm” (width of stem).

I think the intended shape is:

- A rectangle on top: 8 cm × 3 cm
- Attached below it, centered or left-aligned? The “2 cm” is likely the width of the lower rectangle, and “6 cm” its height.
- The “5 cm” might be a red herring or mislabel? Or perhaps it’s the distance from the right edge of the top to the right edge of the bottom?

To avoid confusion, let’s assume the most common L-shape for such problems:

Top: 8 cm wide, 3 cm high
Bottom: 2 cm wide, 6 cm high, attached to the left side of the top rectangle.

So overall shape:

Width: max(8, 2) = 8 cm
Height: 3 + 6 = 9 cm

But the bottom part is only 2 cm wide, so it sticks out on the left? Or right? Usually attached to left.

So coordinates:

Top rectangle: from (0,0) to (8,3)
Bottom rectangle: from (0,3) to (2,9) — so attached at left.

Then outer perimeter:

Start at (0,0):

→ to (8,0): 8 cm
↓ to (8,3): 3 cm
← to (2,3): 6 cm (since bottom starts at x=2)
↓ to (2,9): 6 cm
← to (0,9): 2 cm
↑ to (0,0): 9 cm

Same as before: 8+3+6+6+2+9 = 34 cm

Area: top 8*3=24, bottom 2*6=12, total 36 cm²

And the “5 cm” label — perhaps it’s the length from x=2 to x=8 at y=3? Which is 6 cm, not 5. Maybe typo? Or perhaps the bottom is not 2 cm wide? User said “2 cm” at bottom.

Another possibility: the “5 cm” is the height of the lower part? But it says “6 cm”.

I think we should go with the calculation based on given numbers: 8,3,2,6.

So Area = 8*3 + 2*6 = 24 + 12 = 36 cm²
Perimeter = as calculated 34 cm

But let’s verify perimeter another way: the shape has the following outer sides:

- Top: 8
- Right side: 3 (down)
- Then a horizontal left: 6 (since 8-2=6)
- Then down: 6
- Then left: 2
- Then up: 9 (3+6)
Total: 8+3+6+6+2+9=34

Yes.

✔ A = 36 cm², P = 34 cm

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Problem 7: Irregular hexagon with sides 6 cm, 2 cm, 4 cm, 3 cm, 3 cm, 2 cm, 4 cm? Wait — listed: 6 cm, 2 cm, 4 cm, 3 cm, 3 cm, 2 cm, and another 4 cm? That’s 7 sides? Count the labels.

User wrote: “6 cm, 2 cm, 4 cm, 3 cm, 3 cm, 2 cm, 4cm” — that’s 7 values, but it’s a pentagon? Looking at description: “pentagon” in my earlier thought, but user didn't specify.

From user input: “7. P = _____” and sides: 6 cm, 2 cm, 4 cm, 3 cm, 3 cm, 2 cm, and 4 cm — that’s 7 sides? Impossible for a simple polygon without crossing.

Perhaps it’s a hexagon. List the sides in order as drawn:

Assume the figure has sides: starting from top: 6 cm, then 2 cm, then 4 cm, then 3 cm, then 3 cm, then 2 cm, and back? But that’s 6 sides? 6,2,4,3,3,2 — sum is 6+2+4+3+3+2=20, but there’s also a “4cm” mentioned — perhaps duplicate.

User wrote: “6 cm, 2 cm, 4 cm, 3 cm, 3 cm, 2 cm, 4cm” — probably a mistake. Likely it’s a hexagon with sides 6,2,4,3,3,2 — sum 20 cm.

Or perhaps the last “4cm” is for something else. To resolve, let’s assume the sides are: 6, 2, 4, 3, 3, 2 — that’s six sides, perimeter = 6+2+4+3+3+2 = 20 cm.

If there’s a seventh side, it would be unusual. I think it’s a typo, and it’s six sides.

✔ P = 20 cm

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Problem 8: L-shaped figure, 12 cm height, 9 cm top width, 4 cm right extension, 6 cm inner width.

Describe:

Vertical part: 12 cm high, ? wide
Horizontal part: 9 cm wide, 4 cm high
With a cutout: the inner corner is 6 cm from left?

Standard way: break into two rectangles.

Option 1: large rectangle minus small rectangle.

Overall bounding box: 9 cm wide, 12 cm high → area 108 cm²
Minus the missing rectangle: which is (9 - 6) = 3 cm wide? And (12 - 4) = 8 cm high? Let’s see.

The shape is like:

```
_____________
| | 4 cm
|___________|
| |
| | 8 cm (since 12-4=8)
|_______|
6 cm
```

So the full shape can be seen as:

- Bottom rectangle: 6 cm wide × 12 cm high? No.

Better: the L-shape consists of:

- A vertical rectangle on the left: 6 cm wide × 12 cm high → area 72 cm²
- A horizontal rectangle on the top right: (9 - 6) = 3 cm wide × 4 cm high → area 12 cm²
Total area = 72 + 12 = 84 cm²

Perimeter: trace outer edges.

Start at top-left:

→ right 9 cm
↓ down 4 cm
← left 3 cm (to x=6)
↓ down 8 cm (to y=12)
← left 6 cm
↑ up 12 cm

Sides: 9 + 4 + 3 + 8 + 6 + 12 = let’s add: 9+4=13; 13+3=16; 16+8=24; 24+6=30; 30+12=42 cm

Check: bounding box 9x12 has perimeter 2*(9+12)=42 cm — and since the L-shape has no indentations that add extra perimeter (it’s convex in a way?), actually in this case, the perimeter is the same as the bounding rectangle because the "cut" is internal but we're tracing outer path.

In this path, we have 6 segments, sum 42 cm.

✔ A = 84 cm², P = 42 cm

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Problem 9: U-shaped or C-shaped figure.

Dimensions: overall width? Height 7 cm, then a notch at bottom: 5 cm wide, 2 cm deep, with 3 cm on each side.

So, it’s like a rectangle 7 cm high, and width = 3 + 5 + 3 = 11 cm? But the top is full width.

Shape:

Top: full width, say W = 3 + 5 + 3 = 11 cm
Height: 7 cm
But at the bottom, there’s a rectangular notch removed: 5 cm wide, 2 cm high, centered.

So area = area of big rectangle minus area of notch.

Big rectangle: 11 cm × 7 cm = 77 cm²
Notch: 5 cm × 2 cm = 10 cm²
Area = 77 - 10 = 67 cm²

Perimeter: now, when you remove a notch, you add extra sides.

Original perimeter of 11x7 rectangle: 2*(11+7)=36 cm
But removing a 5x2 rectangle from the bottom center: you remove the bottom side of the notch (5 cm) but add three new sides: two verticals (2 cm each) and the top of the notch (5 cm)? No.

When you cut out a rectangle from the interior of a side, you replace the straight segment with three segments.

Specifically, on the bottom side, instead of a straight 11 cm, you have:

- Left part: 3 cm
- Then down 2 cm
- Then right 5 cm (the bottom of the notch)
- Then up 2 cm
- Then right 3 cm

So compared to original bottom side of 11 cm, you now have: 3 + 2 + 5 + 2 + 3 = 15 cm for the bottom path.

Original bottom was 11 cm, now it’s 15 cm, so increase of 4 cm.

Thus total perimeter = original 36 cm + 4 cm = 40 cm

Calculate directly:

Outer path:

Start at top-left:

→ right 11 cm
↓ down 7 cm
← left 3 cm
↑ up 2 cm (into the notch)
← left 5 cm? No — after going down 7 cm to bottom-right, then left along bottom.

Better:

Start at top-left corner:

1. Right → 11 cm (top)
2. Down → 7 cm (right side)
3. Left → 3 cm (bottom right part)
4. Up → 2 cm (right side of notch)
5. Left → 5 cm (bottom of notch)
6. Down → 2 cm? No, after step 4, you're at the top of the notch on the right, then you go left 5 cm to the left side of the notch, then down 2 cm? That doesn't make sense.

Correct path for U-shape open at bottom:

Actually, the shape is like a rectangle with a bite taken out of the bottom, so it's still connected.

Standard U-shape perimeter:

- Top: 11 cm
- Right side: 7 cm
- Bottom right: 3 cm (horizontal)
- Then up 2 cm (vertical into the notch)
- Then left 5 cm (horizontal across the notch bottom)
- Then down 2 cm? No, after going up 2 cm, you're at the level of the main bottom, then you go left 5 cm, but that would be inside.

I think I have it backward.

If the notch is cut out from the bottom, meaning the bottom has a depression.

So from bottom-right corner:

After coming down the right side 7 cm, you are at (11,7) assuming top-left is (0,0).

Then you go left along the bottom: but there's a notch, so from x=11 to x=8 (3 cm), then down 2 cm to y=9? No, y increases down.

Set coordinate: top-left (0,0), x right, y down.

So:

- From (0,0) to (11,0): top, 11 cm
- (11,0) to (11,7): right side, 7 cm
- (11,7) to (8,7): left 3 cm (bottom right arm)
- (8,7) to (8,9): down 2 cm (right side of notch) — but y=9 is below, so if the shape only goes to y=7, this is wrong.

Mistake: the overall height is 7 cm, and the notch is 2 cm deep, so the bottom of the notch is at y=7 + 2 = 9? But that would make the total height 9 cm, but the label says "7 cm" for the main part.

Looking at user input: "7 cm" on left, "3 cm" on bottom left, "2 cm" for depth, "5 cm" for width of notch, "3 cm" on bottom right.

So likely, the total height is 7 cm for the sides, and the notch is cut into the bottom, so the lowest point is still at y=7, but the notch means that in the middle, it's higher.

Standard interpretation: the figure has a top width of 11 cm (3+5+3), height of 7 cm on the sides, and in the bottom center, there is a rectangular indentation of 5 cm wide and 2 cm deep, so the bottom of the indentation is at y=5 cm (since 7-2=5).

So coordinates:

- Top: y=0, from x=0 to x=11
- Left side: x=0, y=0 to y=7
- Right side: x=11, y=0 to y=7
- Bottom: from x=0 to x=3 at y=7, then up to y=5 at x=3, then right to x=8 at y=5, then down to y=7 at x=8, then right to x=11 at y=7.

So the bottom path is not straight.

Perimeter path:

Start at (0,0):

1. Right to (11,0): 11 cm
2. Down to (11,7): 7 cm
3. Left to (8,7): 3 cm
4. Up to (8,5): 2 cm
5. Left to (3,5): 5 cm
6. Down to (3,7): 2 cm
7. Left to (0,7): 3 cm
8. Up to (0,0): 7 cm

Now sum: 11 + 7 + 3 + 2 + 5 + 2 + 3 + 7 = let's calculate:

11+7=18; 18+3=21; 21+2=23; 23+5=28; 28+2=30; 30+3=33; 33+7=40 cm

Area: as before, big rectangle 11x7=77 cm² minus the notch 5x2=10 cm², so 67 cm².

✔ A = 67 cm², P = 40 cm

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## Final Answers:

1. P = 18 cm
2. A = 14 in², P = 18 in
3. P = 24 cm
4. A = 3880 mm², P = 274 mm
5. A = 52 cm², P = 34 cm
6. A = 36 cm², P = 34 cm
7. P = 20 cm
8. A = 84 cm², P = 42 cm
9. A = 67 cm², P = 40 cm

Final Answer:
1. P = 18 cm
2. A = 14 in², P = 18 in
3. P = 24 cm
4. A = 3880 mm², P = 274 mm
5. A = 52 cm², P = 34 cm
6. A = 36 cm², P = 34 cm
7. P = 20 cm
8. A = 84 cm², P = 42 cm
9. A = 67 cm², P = 40 cm